While you can block someone completely on Facebook, it’s a pretty dramatic measure. Essentially, your Facebook account will cease to exist for them. If you’re just trying to get a bit of a break, you can unfriend them or block them from sending you Facebook Messages so they can’t contact you privately. Here’s how.
On the Website
Open up a chat with the person you want to block.
Click on the Gear icon in the top right and select Block Messages…
Click Block Messages again and they won’t be able to contact you.
To unblock them, just click the Gear icon and then Unblock.
On the Facebook Messenger App
Open the chat with the person you want to block and tap on their name at the top of the screen.
Tap Block and then change the Block Messages toggle to on.
To unblock them, just flip the Block Messages toggle back to off.